OFFSET
1,2
LINKS
FORMULA
From Antti Karttunen, Jan 14 2020: (Start)
a(n) > A056239(n).
gcd(n,a(n)) = A331283(n).
If n = p(k1)^e(k1) * p(k2)^e(k2) * p(k3)^e(k3) * ... * p(kx)^e(kx), with p(n) = A000040(n) and k1 > k2 > ... > kx, then a(n) = (1+e(k1))^(k1-k2) * (1+e(k1)+e(k2))^(k2-k3) * ... * (1+e(k1)+e(k2)+...+e(kx))^kx.
(End)
MATHEMATICA
Block[{a}, a[n_] := a[n] = Module[{f = FactorInteger[n], p, e}, If[Length[f] > 1, Times @@ a /@ Power @@@ f, {{p, e}} = f; Times @@ (Prime[Range[PrimePi[p]]]^e)]]; a[1] = 1; Array[DivisorSigma[0, a@ #] &, 75]] (* Michael De Vlieger, Jan 24 2020, after Jean-François Alcover at A108951 *)
PROG
(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
(PARI) A329605(n) = if(1==n, 1, my(f=factor(n), e=1, m=1); forstep(i=#f~, 1, -1, e += f[i, 2]; m *= e^(primepi(f[i, 1])-if(1==i, 0, primepi(f[i-1, 1])))); (m)); \\ Antti Karttunen, Jan 14 2020
(PARI) A329605(n) = if(1==n, 1, my(f=factor(n), e=0, d); forstep(i=#f~, 1, -1, e += f[i, 2]; d = (primepi(f[i, 1])-if(1==i, 0, primepi(f[i-1, 1]))); f[i, 1] = (e+1); f[i, 2] = d); factorback(f)); \\ Antti Karttunen, Jan 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 18 2019
STATUS
approved